Equation 677 Database

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Magma 504d874c86f3…

magma 504d874c86f3
Size
121
Isomorphism class hash
504d874c86f36ef2c5e84f3b4ecaf75aa0d1d9b76d3756aeba9f68e47e06b864
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
b-reinke
Submitted at
2026-05-13 08:25:11
Display reorder
14,12,1,3,0,11,10,13,2,120,4,18,56,111,61,43,90,35,102,103,42,5,100,88,6,27,119,36,19,57,44,38,62,53,37,58,45,7,15,98,86,117,39,25,84,16,107,115,59,96,54,33,8,40,46,34,94,47,9,105,55,92,17,60,41,113,20,65,83,68,78,30,106,114,95,73,52,112,31,48,93,91,104,21,66,79,74,69,67,109,70,80,49,22,110,32,89,75,101,28,23,99,87,71,118,63,26,50,76,81,108,116,82,51,97,64,29,24,72,77,85 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines partition by line-operation type (in the F_11 parameterization x ◇ y = (1-α)x + αy): 4×α=2 / 8×α=7. • α = 2 on 4 parallel classes (slopes {0, 1, 2, 5}) • α = 7 on 8 parallel classes (slopes {3, 4, 6, 7, 8, 9, 10, INF}) Globally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. Display reorder presents points as (h, v) ∈ F_11 × F_11; the 11 diagonal 11×11 blocks all render as the identical F_11(α=7) Cayley table (the 'horizontal' parallel class). The 11 'vertical' lines (one point per block-row) carry the F_11(α=2) operation. [text written by Claude]

last edited by dwrensha at 2026-05-13 11:45:52 · history